Is a gift that slightly exceeds the value of the debt considered as payment for it, or must the amount be paid in cash?

It is not sufficient to give a gift to repay a loan, because repayment is achieved by giving the exact amount borrowed or its equivalent. If it is anything else, then it is by reconciliation and mutual agreement of both parties. The amount must be paid to the lender, and if he accepts it, then the repayment is complete. If the lender refuses it, then the debtor's responsibility is discharged.